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A368772 a(n) = (n!)^3 * Sum_{k=0..n} (k/k!)^3.

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%I A368772 #17 Jun 14 2025 17:15:11
%S A368772 0,1,16,459,29440,3680125,794907216,272653175431,139598425821184,
%T A368772 101767252423643865,101767252423643866000,135452212975869985647331,
%U A368772 234061424022303335198589696,514232948577000427431301564309,1411055210895289172871491492466640
%N A368772 a(n) = (n!)^3 * Sum_{k=0..n} (k/k!)^3.
%F A368772 a(0) = 0; a(n) = n^3 * a(n-1) + n^3.
%F A368772 a(n) = n^3 * A217284(n-1) for n > 0.
%F A368772 a(n) = Sum_{k=1..n} (k!*binomial(n,k))^3. - _Ridouane Oudra_, Jun 14 2025
%o A368772 (PARI) a(n) = n!^3*sum(k=0, n, (k/k!)^3);
%Y A368772 Cf. A368769, A368770, A368771.
%Y A368772 Cf. A193563, A217284.
%K A368772 nonn,easy
%O A368772 0,3
%A A368772 _Seiichi Manyama_, Jan 05 2024